Is it possible to work on the same blender file at the same time on 2 computers?
There would ultimately be the issue of version control.  If you and your friend were working on the same material, object, at the same time, how would the program decide whose edit to accept?  

There are helps to version control out there like GitHub where a user "checks out" a part of a software project to edit.  While that user is editing, no other user may write to the file, but they can still read from the original file.

With Blender, as far as I understand it, everything (except texture and dependencies) is contained in one solitary .blend file.  That means whoever has it checked out is preventing the other from editing.  

Three things I can think of that might help you with this:

1.) You may use something like LogMeIn or another similar software that would allow you and your friend to have access to the same Desktop via a network/Internet connection.  You would be virtually sharing the same computer and program, but your friend could be in another city/state.

2.) Blender has a nice Append function built in that's accessible from the File menu.  If you could have a central location for storing the .blend file, each of you could "append" objects from that file to your own individual Blender sessions on your respective computers (provided you were working on different objects... i.e. version control), edit them, and then later append them back into the original .blend file.  Of course you would need to collaborate to determine who's working on what and when you would append to the original file.

3.) You could have separate .blend files in a central location, maybe for different objects.  You can then use the Link option to incorporate them into the same master file but edit them individually: https://docs.blender.org/manual/de/dev/data_system/linked_libraries.html
 Again, you'd need to implement VC.

There may be an add-on of some sort that I don't know about that would allow you to do this more easily